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- The boltzmann equation and equilibrium thermodynamics in Lorentz-violating theoriesPublication . Potting, RobertusIn this work, we adapt the foundations of relativistic kinetic theory and the Boltzmann equation to particles with Lorentz-violating dispersion relations. The latter are taken to be those associated to two commonly considered sets of coefficients in the minimal Standard-Model Extension. We treat both the cases of classical (Maxwell-Boltzmann) and quantum (Fermi-Dirac and Bose-Einstein) statistics. It is shown that with the appropriate definition of the entropy current, Boltzmann's H-theorem continues to hold. We derive the equilibrium solutions and then identify the Lorentz-violating effects for various thermodynamic variables, as well as for Bose-Einstein condensation. Finally, a scenario with nonelastic collisions between multiple species of particles corresponding to chemical or nuclear reactions is considered.
- Lorentz symmetry in ghost-free massive gravityPublication . Kostelecký, V. Alan; Potting, RobertusThe role of Lorentz symmetry in ghost-free massive gravity is studied, emphasizing features emerging in approximately Minkowski spacetime. The static extrema and saddle points of the potential are determined and their Lorentz properties identified. Solutions preserving Lorentz invariance and ones breaking four of the six Lorentz generators are constructed. Locally, globally, and absolutely stable Lorentz-invariant extrema are found to exist for certain parameter ranges of the potential. Gravitational waves in the linearized theory are investigated. Deviations of the fiducial metric from the Minkowski metric are shown to lead to pentarefringence of the five wave polarizations, which can include superluminal modes and subluminal modes with negative energies in certain observer frames. The Newton limit of ghost-free massive gravity is explored. The propagator is constructed and used to obtain the gravitational potential energy between two point masses. The result extends the Fierz-Pauli limit to include corrections generically breaking both rotation and boost invariance.
- Standing wave solutions in Born-Infeld theoryPublication . Manojlovic, Nenad; Perlick, Volker; Potting, RobertusWe study standing-wave solutions of Born-Infeld electrodynamics, with nonzero electromagnetic field in a region between two parallel conducting plates. We consider the simplest case which occurs when the vector potential describing the electromagnetic field has only one nonzero component depending on time and on the coordinate perpendicular to the plates. the problem then reduces to solving the scalar Born-Infeld equation, a nonlinear partial differential equation in 1+1 dimensions. We apply two alternative methods to obtain standing-wave solutions to the Born-Infeld equation: an iterative method, and a "minimal surface" method. We also study standing wave solutions in a uniform constant magnetic field background. the results obtained in this work provide a theoretical background for experimental tests of Born-Infeld theory. (C) 2020 Elsevier Inc. All rights reserved.
- Degenerate behavior in nonlinear vacuum electrodynamicsPublication . Escobar, C. A.; Potting, RobertusWe study nonlinear vacuum electrodynamics in the first-order formulation proposed by Plebanski. We analyze in detail the equations of motion, and identify conditions for which a singularity can occur for the time derivative of one of the field components. The resulting degenerate behavior can give rise to a shock wave with a reduction of the local number of degrees of freedom. We use an example model to illustrate the occurrence of superluminal propagation for field values approaching the singularity.
- Nonlinear vacuum electrodynamics and spontaneous breaking of Lorentz symmetryPublication . Escobar, C. A.; Potting, RobertusWe study spontaneous breaking of Lorentz symmetry in nonlinear vacuum electrodynamics. Using a first-order formulation of the latter proposed by Plebanski, we apply a Dirac constraint analysis and derive an effective Hamiltonian. We show that there exists a large class of potentials for which the effective Hamiltonian is bounded from below, while at the same time possessing local minima in which the field strength acquires a nonzero vacuum expectation value, thereby breaking Lorentz invariance spontaneously. These possible vacua can be classified in four classes, depending on the way Lorentz symmetry is broken. We show that the small field fluctuations around these vacua involve modes for which the dynamics can develop degeneracies, resulting in shock-wave-like and/or superluminal motion. Finally, we study the physical applicability of these models, and show how the Lorentz breaking vacua might in principle be detected by coupling the model to a suitable external current, or to gravity.
- Bounding CPT and Lorentz symmetry violations through ultra-high-energy cosmic raysPublication . Escobar, C A; Potting, RobertusWe review recent work on CPT and Lorentz violation in the context of the Standard-Model Extension. In particular, we show that, when CPT and Lorentz violation is present in the kinetic terms of any particle in the gauge boson or the lepton sector, this will generally lead to proton decay at sufficiently high energy. Using observational data from ultra-high energy cosmic rays, this has allowed to derive new bounds on the corresponding CPT and Lorentz-violation parameters.
- Coupled quintessence with a generalized interaction termPublication . Potting, Robertus; Sá, PauloWe investigate a cosmological model in which dark energy, represented by a quintessential scalar field, is directly coupled to a dark-matter perfect fluid. We are interested in solutions of cosmological relevance, namely those for which a dark-matter-dominated era long enough to allow for structure formation is followed by an era of accelerated expansion driven by dark energy. For the coupling between these two dark components of the Universe, we choose forms that generalize the one most commonly used in the literature. Resorting to powerful methods of qualitative analysis of dynamical systems, we show that, for certain generalized forms of the coupling, final states of our coupled quintessential model correspond to solutions in which the evolution of the Universe is completely dominated by dark energy. In this case, there are no scaling solutions. Interestingly, however, for certain values of a relevant parameter, during the approach to the final state of evolution, the cosmological parameters change so slowly that, for all practical purposes, the solution appears to be stuck in a state corresponding to a scaling solution.
- Stable Lorentz-breaking model for an antisymmetric two-tensorPublication . Potting, RobertusIn this work we investigate possible actions for antisymmetric two-tensor field models subject to constraints that force the field to acquire a nonzero vacuum expectation value, thereby spontaneously breaking Lorentz invariance. In order to assure stability, we require that the associate Hamiltonian be bounded from below. It is shown that this requirement rules out any quadratic action constructed only from the antisymmetric tensor field. We then explicitly construct a hybrid model consisting of the antisymmetric two-tensor field together with a vector field, subject to constraints forcing nonzero expectation values, that is stable in Minkowski space.